# A simple theoretical analysis of the carrier contribution to the elastic constants in quantum wires of IV-VI semiconductors in the presence of a parallel magnetic field

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TL;DR: In this paper, the thermoelectric power in the presence of a large magnetic field (TPM) in heavily doped III-V, II-VI, PbTe/PbSnTe, strained layer and HgTe/CdTe quantum dot superlattices (QDSLs) with graded structures was analyzed.

Abstract: We study theoretically the thermoelectric power in the presence of a large magnetic field (TPM) in heavily doped III–V, II–VI, PbTe/PbSnTe, strained layer and HgTe/CdTe quantum dot superlattices (QDSLs) with graded structures on the basis of newly formulated electron energy spectra and compare the same with that of the constituent materials. It has been found, taking heavily doped GaAs/Ga1−xAlxAs, CdS/CdTe, PbTe/PbSnTe, InAs/GaSb and HgTe/CdTe QDSLs as examples, that the TPM increases with increasing inverse electron concentration and film thickness, respectively, in different oscillatory manners and the nature of oscillations is totally band structure dependent. We have also suggested the experimental methods of determining the Einstein relation for the diffusivity–mobility ratio, the Debye screening length and the electronic contribution to the elastic constants for materials having arbitrary dispersion laws.

21 citations

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TL;DR: In this article, a simple theoretical analysis of the effective electron mass (EEM) at the Fermi level for III-V, ternary and quaternary materials, on the basis of a newly formulated electron energy spectra in the presence of light waves whose unperturbed energy band structures are defined by the three-band model of Kane, is presented.

Abstract: We present a simple theoretical analysis of the effective electron mass (EEM) at the Fermi level for III–V, ternary and quaternary materials, on the basis of a newly formulated electron energy spectra in the presence of light waves whose unperturbed energy band structures are defined by the three-band model of Kane The solution of the Boltzmann transport equation on the basis of this newly formulated electron dispersion law will introduce new physical ideas and experimental findings under different external conditions It has been observed that the unperturbed isotropic energy spectrum in the presence of light changes into an anisotropic dispersion relation with the energy-dependent mass anisotropy In the presence of light, the conduction band moves vertically upward and the band gap increases with the intensity and colours of light It has been found, taking n-InAs, n-InSb, n-Hg1−xCdxTe and n-In1−xGaxAsyP1−y lattice matched to InP as examples, that the EEM increases with increasing electron concentration, intensity and wavelength in various manners The strong dependence of the effective momentum mass (EMM) at the Fermi level on both the light intensity and wavelength reflects the direct signature of the light waves which is in contrast with the corresponding bulk specimens of the said materials in the absence of photo-excitation The rate of change is totally band-structure-dependent and is influenced by the presence of the different energy band constants The well known result for the EEM at the Fermi level for degenerate wide gap materials in the absence of light waves has been obtained as a special case of the present analysis under certain limiting conditions, and this compatibility is the indirect test of our generalized formalism

19 citations

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TL;DR: In this article, the energy spectrum of conduction electrons and the corresponding density-of-states (DOS) in heavily doped compound semiconductors forming band-tails were studied.

Abstract: We study the energy spectrum of the conduction electrons and the corresponding density-of-states (DOS) in heavily doped compound semiconductors forming band-tails. It is found, taking Hg 1− x Cd x Te as an example, that the complex nature of the energy spectrum, the oscillatory DOS for negative values of the energy and the formation of a new forbidden zone is due to interaction of the impurity atoms in the tail with the spin–orbit splitting constant of the valence band. No oscillations in the DOS are found for heavily doped two-band Kane type and parabolic energy bands, respectively. The well-known results have also been obtained from our generalized derivation under certain limiting conditions.

16 citations

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TL;DR: In this article, a simple theoretical analysis of the carrier contribution to the second and third order elastic constants in nonparabolic materials on the basis of an electron dispersion law by taking into account various anisotropies of the energy band structure was presented.

Abstract: We present a simple theoretical analysis of the carrier contribution to the second and third order elastic constants in nonparabolic materials on the basis of an electron dispersion law by taking into account various anisotropies of the energy band structure within the framework of k⋅p formalism. It is found that the carrier contributions to the elastic constants in n-Cd3As2, InSb, InAs, GaAs, Hg1−xCdxTe, and lattice matched In1−xGaxAsyP1−y increase with the increase of carrier degeneracy in different manners which, depend on the material parameters and band structure. A relationship between the said contributions and the thermoelectric power has been derived for materials obeying arbitrary dispersion laws in the presence of a classically large magnetic field. Our analysis is based on the derivation of a more generalized band structure of the materials which agrees well with the relationship suggested. It is also observed that the second and third order elastic constants increase with the decrease of allo...

15 citations

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TL;DR: In this article, the influence of light waves on the thermoelectric power under large magnetic field (TPM) for III-V, ternary and quaternary materials, whose unperturbed energy-band structures, are defined by the three-band model of Kane.

Abstract: We study theoretically the influence of light waves on the thermoelectric power under large magnetic field (TPM) for III-V, ternary and quaternary materials, whose unperturbed energy-band structures, are defined by the three-band model of Kane. The solution of the Boltzmann transport equation on the basis of this newly formulated electron dispersion law will introduce new physical ideas and experimental findings in the presence of external photoexcitation. It has been found by taking n-InAs, n-InSb, n-Hg1-xCdxTe and n-In1-xGaxAsyP1-y lattice matched to InP as examples that the TPM decreases with increase in electron concentration, and increases with increase in intensity and wavelength, respectively in various manners. The strong dependence of the TPM on both light intensity and wavelength reflects the direct signature of light waves that is in direct contrast as compared with the corresponding bulk specimens of the said materials in the absence of external photoexcitation. The rate of change is totally band-structure dependent and is significantly influenced by the presence of the different energy-band constants. The well-known result for the TPM for nondegenerate wide-gap materials in the absence of light waves has been obtained as a special case of the present analysis under certain limiting conditions and this compatibility is the indirect test of our generalized formalism. Besides, we have also suggested the experimental methods of determining the Einstein relation for the diffusivity:mobility ratio, the Debye screening length and the electronic contribution to the elastic constants for materials having arbitrary dispersion laws.

13 citations

##### References

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06 May 1980

TL;DR: In this paper, the Boltzmann Transport Equation is used to calculate the collision probability of the Sphalerite and the Chalcopyrite structures, and the Brillouin Zone is used for the Wurtzite structure.

Abstract: 1. Introduction.- 1.1 Historical Note.- 1.2 Applications.- 1.3 Transport Coefficients of Interest.- 1.4 Scope of the Book.- 2. Crystal Structure.- 2.1 Zinc-Blende Structure.- 2.2 Wurtzite Structure.- 2.3 Rock-Salt Structure.- 2.4 Chalcopyrite Structure.- 3. Energy Band Structure.- 3.1 Electron Wave Vector and Brillouin Zone.- 3.2 Brillouin Zone for the Sphalerite and Rock-Salt Crystal Structure.- 3.3 Brillouin Zone for the Wurtzite Structure.- 3.4 Brillouin Zone for the Chalcopyrite Structure.- 3.5 E-k Diagrams.- 3.5.1 Energy Bands for the Sphalerite Structure.- 3.5.2 Energy Bands for the Wurtzite Structure.- 3.5.3 Energy Bands for the Rock-Salt Structure.- 3.5.4 Band Structure of Mixed Compounds.- 3.6 Conclusion.- 4. Theory of Efiergy Band Structure.- 4.1 Models of Band Structure.- 4.2 Free-Electron Approximation Model.- 4.3 Tight-Binding Approximation Model.- 4.4 Energy Bands in Semiconductor Super!attices.- 4.5 The k-p Perturbation Method for Derivating E-k Relation.- 4.5.1 Single-Band Perturbation Theory.- 4.5.2 Two-Band Approximation.- 4.5.3 Effect of Spin-Orbit Interaction.- 4.5.4 Nonparabolic Relation for Extrema at Points Other than the r Point.- 4.6 External Effects on Energy Bands.- 4.6.1 Effects of Doping.- 4.6.2 Effects of Large Magnetic Fields.- 5. Electron Statistics.- 5.1 Fermi Energy for Parabolic Bands.- 5.2 Fermi Energy for Nonparabolic Bands.- 5.3 Fermi Energy in the Presence of a Quantising Magnetic Field.- 5.3.1 Density of States.- 5.3.2 Fermi Level.- 5.4 Fermi Energy and Impurity Density.- 5.4.1 General Considerations.- 5.4.2 General Formula.- 5.4.3 Discussion of Parabolic Band.- 5.4.4 Effect of Magnetic Field.- 5.5 Conclusions.- 6. Scattering Theory.- 6.1 Collision Processes.- 6.2 Transition Probability.- 6.3 Matrix Elements.- 6.4 Free-Carrier Screening.- 6.5 Overlap Integrals.- 6.6 Scattering Probability S(k).- 6.6.1 S(k) for Ionised Impurity Scattering.- 6.6.2 S(k) for Piezoelectric Scattering.- 6.6.3 S(k) for Deformation-Potential Acoustic Phonon Scattering.- 6.6.4 S(k) for Polar Optic Phonon Scattering.- 6.6.5 S(k) for Intervalley and Nonpolar Optic Phonon Scattering.- 6.7 Scattering Probabilities for Anisotropic Bands.- 6.7.1 Herring-Vogt Transformation.- 6.7.2 Scattering Integrals.- 6.8 S(k) for Neutral Impurity, Alloy, and Crystal-Defect Scattering.- 6.8.1 Neutral-Impurity Scattering.- 6.8.2 Alloy Scattering.- 6.8.3 Defect Scattering.- 6.9 Conclusions.- 7. The Boltzmann Transport Equation and Its Solution.- 7.1 The Liouville Equation and the Boltzmann Equation.- 7.2 The Boltzmann Transport Equation.- 7.3 The Collision Integral.- 7.4 Linearised Boltzmann Equation.- 7.5 Simplified Form of the Collision Terms.- 7.5.1 Collision Terms for Elastic Scattering.- 7.5.2 Collision Terms for Inelastic Scattering.- 7.6 Solution of the Boltzmann Equation.- 7.6.1 Relaxation-Time Approximation.- 7.6.2 Variational Method.- 7.6.3 Matrix Method.- 7.6.4 Iteration Method.- 7.6.5 Monte Carlo Method.- 7.7 Method of Solution for Anisotropic Coupling Constants and Anisotropic Electron Effective Mass.- 7.7.1 Solution for Elastic Collisions.- 7.7.2 Solution for Randomising Collisions.- 7.7.3 Solution for Nonrandomising Inelastic Collisions.- 7.8 Conclusions.- 8. Low-Field DC Transport Coefficients.- 8.1 Evaluation of Drift Mobility.- 8.1.1 Formulae for Relaxation-Time Approximation.- 8.1.2 Evaluation by the Variational Method.- 8.1.3 Evaluation by Matrix and Iteration Methods.- 8.1.4 Evaluation by the Monte Carlo Method.- 8.2 Drift Mobility for Anisotropic Bands.- 8.2.1 Ellipsoidal Band.- 8.2.2 Warped Band.- 8.3 Galvanomagnetic Transport Coefficients.- 8.3:1 Formulae for Hall Coefficient, Hall Mobility, and Magnetoresistance.- 8.3.2 Reduced Boltzmann Equation for the Galvanomagnetic Coefficients.- 8.3.3 Solution Using the Relaxation-Time Approximation Method.- 8.3.4 A Simple Formula for the Low-Field Hall Mobility.- 8.3.5 Numerical Methods for the Galvanomagnetic Coefficients for Arbitrary Magnetic Fields.- 8.3.6 Evaluation of the Galvanomagnetic Transport Coefficients for Anisotropic Effective Mass.- 8.4 Transport Coefficients for Nonuniform conditions.- 8.4.1 Diffusion.- 8.4.2 Thermal Transport Coefficients.- 8.4.3 Formula for Thermoelectric Power.- 8.4.4 Electronic Thermal Conductivity.- 8.5 Conclusions.- 9. Low-Field AC Transport Coefficients.- 9.1 Classical Theory of AC Transport Coefficients.- 9.1.1 Solution for the Relaxation-Time Approximation.- 9.1.2 Solution for Polar Optic Phonon and Mixed Scattering.- 9.1.3 Solution for Nonparabolic and Anisotropic Bands.- 9.2 AC Galvanomagnetic Coefficients.- 9.3 Cyclotron Resonance and Faraday Rotation.- 9.3.1 Propagation of Electromagnetic Waves in a Semiconductor in the Presence of a Magnetic Field.- 9.3.2 Cyclotron Resonance Effect.- 9.3.3 Faraday Rotation.- 9.4 Free-Carrier Absorption (FCA).- 9.4.1 Classical Theory of FCA.- 9.4.2 Quantum-Mechanical Theory of FCA.- 9.5 Concluding Remarks.- 10. Electron Transport in a Strong Magnetic Field.- 10.1 Scattering Probabilities.- 10.2 Mobility in Strong Magnetic Fields.- 10.3 Electron Mobility in the Extreme Quantum Limit (EQL).- 10.3.1 Electron Mobility for Polar Optic Phonon Scattering in the EQL.- 10.4 Oscillatory Effects in the Magnetoresistance.- 10.4.1 Shubnikov-de Haas Effect.- 10.4.2 Magnetophonon Oscillations.- 10.5 Experimental Results on Magnetophonon Resonance.- 10.6 Conclusions.- 11. Hot-Electron Transport.- 11.1 Phenomenon of Hot Electrons.- 11.2 Experimental Characteristics.- 11.3 Negative Differential Mobility and Electron Transfer Effect.- 11.4 Analytic Theories.- 11.4.1 Differential Equation Method.- 11.4.2 Maxwellian Distribution Function Method.- 11.4.3 Displaced Maxwellian Distribution Function Method.- 11.5 Numerical Methods.- 11.5.1 Iteration Method.- 11.5.2 Monte Carlo Method.- 11.6 Hot-Electron AC Conductivity.- 11.6.1 Phenomenological Theory for Single-Valley Materials.- 11.6.2 Phenomenological Theory for Two-Valley Materials.- 11.6.3 Large-Signal AC Conductivity.- 11.7 Hot-Electron Diffusion.- 11.7.1 Einstein Relation for Hot-Electron Diffusivity.- 11.7.2 Electron Diffusivity in Gallium Arsenide.- 11.7.3 Monte Carlo Calculation of the Diffusion Constant.- 11.8 Conclusion.- 12. Review of Experimental Results.- 12.1 Transport Coefficients of III-V Compounds.- 12.1.1 Indium Antimonide.- 12.1.2 Gallium Arsenide.- 12.1.3 Indium Phosphide.- 12.1.4 Indium Arsenide.- 12.1.5 Indirect-Band-Gap III-V Compounds.- 12.2 II-VI Compounds.- 12.2.1 Cubic Compounds of Zinc and Cadmium.- 12.2.2 Wurtzite Compounds of Zinc and Cadmium.- 12.2.3 Mercury Compounds.- 12.3 IV-VI Compounds.- 12.4 Mixed Compounds.- 12.5 Chalcopyrites.- 12.6 Conclusion.- 13. Conclusions.- 13.1 Problems of Current Interest.- 13.1.1 Heavily Doped Materials.- 13.1.2 Alloy Semiconductors.- 13.1.3 Transport Under Magnetically Quantised Conditions.- 13.1.4 Inversion Layers.- 13.1.5 Superlattices and Heterostructures.- 13.2 Scope of Further Studies.- Appendix A: Table of Fermi Integrals.- Appendix B: Computer Program for the Evaluation of Transport Coefficients by the Iteration Method.- Appendix C: Values of a. and b. for Gaussian Quadrature Integration. 417 Appendix D: Computer Program for the Monte Carlo Calculation of Hot-Electron Conductivity and Diffusivity.- List of Symbols.- References.

680 citations

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01 Jan 1990

TL;DR: The proceedings of the NATO Advanced Research Workshop on the Science and Engineering of 1 and O-dimensional semiconductors held at the University of Cadiz from 29th March to 1st April 1989, under the auspices of theNATO International Scientific Exchange Program as discussed by the authors.

Abstract: This volume comprises the proceedings of the NATO Advanced Research Workshop on the Science and Engineering of 1- and O-dimensional semiconductors held at the University of Cadiz from 29th March to 1st April 1989, under the auspices of the NATO International Scientific Exchange Program. There is a wealth of scientific activity on the properties of two-dimensional semiconductors arising largely from the ease with which such structures can now be grown by precision epitaxy techniques or created by inversion at the silicon-silicon dioxide interface. Only recently, however, has there burgeoned an interest in the properties of structures in which carriers are further confined with only one or, in the extreme, zero degrees of freedom. This workshop was one of the first meetings to concentrate almost exclusively on this subject: that the attendance of some forty researchers only represented the community of researchers in the field testifies to its rapid expansion, which has arisen from the increasing availability of technologies for fabricating structures with small enough (sub - O. I/tm) dimensions. Part I of this volume is a short section on important topics in nanofabrication. It should not be assumed from the brevity of this section that there is little new to be said on this issue: rather that to have done justice to it would have diverted attention from the main purpose of the meeting which was to highlight experimental and theoretical research on the structures themselves.

104 citations

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TL;DR: In this paper, an attempt is made to study the effective electron mass in strained layer superlattices of non-parabolic semiconductors with graded structures under sirong magnetic quantization and to compare the same with the bulk specimens of the constituent materials, by formulating the appropriate magneto-dispersion laws.

Abstract: An attempt is made to study the effective electron mass in strained layer superlattices of non-parabolic semiconductors with graded structures under sirong magnetic quantization and to compare the same with the bulk specimens of the constituent materials, by formulating the appropriate magneto-dispersion laws. It is found, taking InAs/GaSb superlattice as an example, that the effective electron mass oscillates with the inverse quantizing magnetic field due to the Shubnikov-de Hass effect. The dependence of the effective mass on the magnetic quantum number in addition to Fermi energy is an intrinsic property of such semiconductor heterostructures. The stress makes the mass quantum number dependent in bulk specimens and even in the presence of broadening, the effective masses in superlattices exhibit significant oscillations with enhanced numerical values from that of the constituent semiconductors. Besides the effective electron masses also increase in an oscillatory way with increasing electron c...

38 citations

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TL;DR: In this paper, the photoemission from ultrathin films, quantum wires and quantum dots of degenerate Kane-type semiconductors, respectively, on the basis of a newly derived dispersion relation of the conduction electrons allowing all types of anisotropies of the band parameters within the framework of k⋅p formalism was investigated.

Abstract: An attempt is made to investigate the photoemission from ultrathin films, quantum wires and quantum dots of degenerate Kane‐type semiconductors, respectively, on the basis of a newly derived dispersion relation of the conduction electrons allowing all types of anisotropies of the band parameters within the framework of k⋅p formalism. It is found, taking n‐Cd3As2 as an example, that the photoemission increases with increasing photon energy in a ladderlike manner and also exhibits oscillatory dependences with changing electron concentration and film thickness, respectively, for all types of quantum confinement. The photoemitted current density is greatest for quantum dots and least for ultrathin films in all the cases. In addition, the well‐known results for bulk specimens of parabolic semiconductors have also been obtained from the generalized expressions under certain limiting conditions.

28 citations